Mécanique Quantique Relativiste

This course aims to provide a general overview of relativistic quantum mechanics. The key element is the bringing together of quantum theory and special relativity.

This handout is intended mainly for third year undergraduate students according to the LMD system program.

Cours Content

Chapter 1: Klein-Gordon equation
 Derivation using the correspondence principle
 Continuity equation
 Solution for a free particle
 Coupling with the electromagnetic field
 Solution of the Klein-Gordon equation in a Coulomb field
 Defects of the Klein-Gordon equation
Chapter 2: Dirac equation
 Derivation of the Dirac equation
 Continuity equation
 Properties of Dirac matrices
 The covariant form of Dirac equation
 Coupling with the electromagnetic field
 The non-relativistic limit: Pauli equation
 Lorentz transformations
 Covariance and spinor transformation
 Bilinears
 General solution of Dirac equation for a free particle
 Relations of orthogonality
  Projection operators of Energy
 Orbital angular momentum and spin
 Spin projection operators
Chapter 3: Physical interpretation of solutions to Dirac equation
 Wave packets, positive and negative energy states
 The Zitterbewegung “tremor effect”
 Klein's paradox
 The theory of holes
Chapter 4: The Symmetries of Dirac Equation
 Translation
 Rotation
 Special Lorentz transformation (boost)
 Parity
 Reversal of time
 Conjugation of charge
 Helicity and chirality
 Gauge transformation
 Weyl’s equation